Stoica, Ovidiu Cristinel (2022) Born rule: quantum probability as classical probability. [Preprint]
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Abstract
I provide a simple derivation of the Born rule as giving a classical probability, that is, the ratio of the measure of favorable states of the system to the measure of its total possible states.
In classical systems, the probability is due to the fact that the same macro state can be realized in different ways as a micro state. Despite the radical differences between quantum and classical systems, the same can be applied to quantum systems. More precisely, I show that in a continuous basis, the contributing basis vectors are present in a state vector with real and equal coefficients, but they are distributed with variable density among the eigenspaces of the observable. The measure of the contributing basis vectors gives the Born rule without making other assumptions.
This works only if the basis is continuous, but all known physically realistic measurements involve a continuous basis, because they involve the positions of the particles.
The continuous basis is not unique, and for subsystems it depends on the observable.
But for the entire universe, there are continuous bases that give the Born rule for all measurements, because all measurements reduce to distinguishing macroscopic pointer states, and macroscopic observations commute. This allows for the possibility of an ontic basis for the entire universe.
In the wavefunctional formulation, the basis can be chosen to consist of classical field configurations, and the coefficients Ψ[ϕ] can be made real by absorbing them into a global U(1) gauge.
This suggests an interpretation of the wavefunction as a nonuniform distribution of classical states. For the manyworlds interpretation, this result gives the Born rule from microbranch counting.
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Item Type:  Preprint  

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Keywords:  Born rule; state counting; Everett's interpretation; manyworlds interpretation; branch counting.  
Subjects:  Specific Sciences > Physics > Quantum Mechanics  
Depositing User:  Ovidiu Cristinel Stoica  
Date Deposited:  02 Nov 2022 21:21  
Last Modified:  02 Nov 2022 21:21  
Item ID:  21349  
Subjects:  Specific Sciences > Physics > Quantum Mechanics  
Date:  18 September 2022  
URI:  https://philsciarchive.pitt.edu/id/eprint/21349 
Available Versions of this Item

Born rule from counting states. (deposited 18 Sep 2022 19:42)

Born rule from counting states. (deposited 07 Oct 2022 13:46)

Born rule from counting states. (deposited 08 Oct 2022 15:24)
 Born rule: quantum probability as classical probability. (deposited 02 Nov 2022 21:21) [Currently Displayed]

Born rule from counting states. (deposited 08 Oct 2022 15:24)

Born rule from counting states. (deposited 07 Oct 2022 13:46)
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